Only AHC. Some will say it will last forever if properly maintained while others won't buy an LX because of the inevitable costly replacement or conversion to a standard suspension. Lots of threads on it if you do a search.
Other than that, I believe they are identical in performance. LX may require premium while LC runs fine on 87, but not 100% on that.
AHC accumulators will eventually wear out as well as the shocks/rams, and none of that is cheap at dealer or discounted prices. Changing to standard suspension can be relatively cheap if you can find used torsion bars. If it's working right, it's really nice feature.
LX's most defintely can run on 87 octane.
My LX is adequately comfortable on 100 mile drives with 5 adults in the front and middle seats...not sure I'd try a longer road trip. 
and I, not to mention you can do more than you thought an SUV could do on a twisty road, through ice and snow, and see overall generally better reliability. We can still fit a dog or 2 in the back and more than enough stuff in the very back if we go out to get some birds or a deer.